Effect and Treatment of Long-Range Forces in the Theory of Nuclear Matter

Abstract

The effect and treatment fo the long-range part of nuclear forces in the theory of nuclear matter is discussed. From a study of the matrix elements of this potential $v_l$, the diverse contributions of $v_l$ to first order (-38 MeV), second order (-1 MeV), third order (-5 MeV), etc. are reconciled to each other. The ideas are then extended to all three-body, four-body, and higher-cluster diagrams of all orders in perturbation, where it is shown that the leading contribution of $v_l$ comes from diagrams containing only one long-range interaction and the rest short range. It is also shown that this long-range interaction must occur in diagonal form, i.e., as a "bubble insert." It is finally pointed out that, using the familiar Hartree method, these bubble inserts can be included in the single-particle energies, thereby absorbing most of the effect of $v_l$ on higher clusters.